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function Depth-Limited-Search-Backward(u, Δ, B, F) is prepend u to B if Δ = 0 then if u in F then return u (Reached the marked node, use it as a relay node) remove the head node of B return null foreach parent of u do μ ← Depth-Limited-Search-Backward(parent, Δ − 1, B, F) if μ null then return μ remove the head node of B return null
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
In depth-first search (DFS), the search tree is deepened as much as possible before going to the next sibling. To traverse binary trees with depth-first search, perform the following operations at each node: [3] [4] If the current node is empty then return. Execute the following three operations in a certain order: [5] N: Visit the current node.
It also maintains a value v.lowlink that represents the smallest index of any node on the stack known to be reachable from v through v's DFS subtree, including v itself. Therefore v must be left on the stack if v.lowlink < v.index, whereas v must be removed as the root of a strongly connected component if v.lowlink == v.index.
An efficient implementation using a disjoint-set data structure can perform each union and find operation on two sets in nearly constant amortized time (specifically, (()) time; () < for any plausible value of ), so the running time of this algorithm is essentially proportional to the number of walls available to the maze.
Iterative-deepening-A* works as follows: at each iteration, perform a depth-first search, cutting off a branch when its total cost () = + exceeds a given threshold.This threshold starts at the estimate of the cost at the initial state, and increases for each iteration of the algorithm.
The breadth-first-search algorithm is a way to explore the vertices of a graph layer by layer. It is a basic algorithm in graph theory which can be used as a part of other graph algorithms.
Robot in a wooden maze. A maze-solving algorithm is an automated method for solving a maze.The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see the whole maze at once.
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